Giải thích các bước giải:
Ta có:
$\dfrac{CM}{MD}=\dfrac{S_{CBM}}{S_{BDM}}=\dfrac{S_{KMC}}{S_{KMD}}=\dfrac{S_{CMB}+S_{CMK}}{S_{BDM}+S_{DKM}}=\dfrac{S_{KCD}}{S_{BCD}}$
Tương tự:
$\dfrac{CN}{NB}=\dfrac{S_{KBC}}{S_{BCD}}$
$\to \dfrac{CM}{MD}+\dfrac{CN}{ND}=\dfrac{S_{KBC}+S_{KCD}}{S_{BCD}}$
Mà $\dfrac{CK}{CI}=\dfrac{S_{CDK}}{S_{CID}}=\dfrac{S_{CKB}}{S_{CIB}}=\dfrac{S_{KCD}+S_{KBC}}{S_{CID}+S_{CIB}}=\dfrac{S_{KBC}+S_{KCD}}{S_{BCD}}$
$\to \dfrac{CM}{MD}+\dfrac{CN}{ND}=\dfrac{CK}{CI}$